Question

given AD=BE=CF .Prove that ABC is equilateral triangle
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Answer 1

Answer:

Step-by-step explanation:

In ΔABC:

› AD/BE/CF

RTP:

› ΔABC is a equilateral triangle.

Proof:

Consider ΔABE & ΔACF:

› BE = CF (Given)

› ∠A = ∠A (Common)

› ∠AEB = ∠AFC = 90° (Right angled triangles)

∴ ABE ≅ ACF (AAS)

AB = AC (C.P.C.T)

[Corresponding parts of congruent triangles]

So, BCF ≅ ABD

[Corresponding sides of congruent triangles are equal]

› AB = BC  

› AC = BC  

› AB = AC

[All sides are equal, it is a equilateral triangle]

∴ AB = BC = AC, ΔABC is a equilateral triangle.

Answer 2

Answer refers in attachment.

it helps you.